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Simplifying 4x2 + 16x + -27 = 0 Reorder the terms: -27 + 16x + 4x2 = 0 Solving -27 + 16x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.75 + 4x + x2 = 0 Move the constant term to the right: Add '6.75' to each side of the equation. -6.75 + 4x + 6.75 + x2 = 0 + 6.75 Reorder the terms: -6.75 + 6.75 + 4x + x2 = 0 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + 4x + x2 = 0 + 6.75 4x + x2 = 0 + 6.75 Combine like terms: 0 + 6.75 = 6.75 4x + x2 = 6.75 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 6.75 + 4 Reorder the terms: 4 + 4x + x2 = 6.75 + 4 Combine like terms: 6.75 + 4 = 10.75 4 + 4x + x2 = 10.75 Factor a perfect square on the left side: (x + 2)(x + 2) = 10.75 Calculate the square root of the right side: 3.278719262 Break this problem into two subproblems by setting (x + 2) equal to 3.278719262 and -3.278719262.Subproblem 1
x + 2 = 3.278719262 Simplifying x + 2 = 3.278719262 Reorder the terms: 2 + x = 3.278719262 Solving 2 + x = 3.278719262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.278719262 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.278719262 + -2 x = 3.278719262 + -2 Combine like terms: 3.278719262 + -2 = 1.278719262 x = 1.278719262 Simplifying x = 1.278719262Subproblem 2
x + 2 = -3.278719262 Simplifying x + 2 = -3.278719262 Reorder the terms: 2 + x = -3.278719262 Solving 2 + x = -3.278719262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.278719262 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.278719262 + -2 x = -3.278719262 + -2 Combine like terms: -3.278719262 + -2 = -5.278719262 x = -5.278719262 Simplifying x = -5.278719262Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.278719262, -5.278719262}
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